This invention relates to circuits and methods for measuring a mean square value of a signal having a known fundamental frequency and a low even harmonic content. This invention particularly relates to providing a mean square value of 60 Hertz current and related parameters in a power distribution line.
Power distribution lines provide alternating current at a frequency which is closely controlled and maintained at 60 Hertz. The generation and distribution line system is such that even harmonics are minimal.
To preserve the ability of a power distribution system to distribute power a number of protective devices are employed. The ability of the power system to distribute power is contingent on a number of factors. A factor of considerable significance is the extent to which the system elements should dissipate energy. A measure of the energy that should be dissipated is provided by the mean square of the current conducted by the system multiplied by the time the system is conducting the current. A plot of a mean square current and time for a protective device to act is known as its time current characteristic. Many types of protective devices measure the value of line current conducted by them and operate to interrupt the line current when it is excessive or faulted. These protective devices may measure the true root mean square value of line current but more often measure an equivalent mean square value. The equivalent means square value may be PG,3 generated by a peak sensing circuit and applying a form factor. Peak sensing is not considered to be particularly accurate because a single form factor is not appropriate for normal and all fault currents.
Most power distribution lines have three phases and it is desirable to measure line current in each phase and ground to protect the system. Rather than providing four measuring means, one for each phase and ground, the phase and ground sensors can be multiplexed and presented to a single measuring means.
Multiplexing usually requires that a signal be periodically sampled at an appropriate rate to preserve its essential characteristics. It is believed that the parameters for sampling and preserving the essential characteristics were first developed in the communications field. The work of C. E. Shannon and H. Nyquist provide the basic criteria for sampling. In general, Nyquist demonstrated that a sampling frequency which is twice the value of the highest frequency of the sampled signal will preserve the essential characteristic of the sample signal. If the signal to be sampled contains frequency components which are greater than the Nyquist Frequency or half the sampling frequency; not only will information relating to the higher frequencies be lost, but an error affecting the accuracy of the lower frequencies is introduced. These errors are referred to as aliasing errors. In many applications, absolute accuracy of the sampled values is not required. In some cases aliasing error was ignored. In others, a low pass filter was inserted before a sampling means to eliminate higher frequency components of the signal to those no greater than half the sampling rate. This low pass filter compromise also introduces filter errors involving a frequency dependent phase shift and amplitude error. As a result of the existence of aliasing errors and filter errors, devices employing sampling means were generally designed to sample at the highest frequency possible in an attempt to minimize these errors.
Those attempting to measure current and associated parameters in power distribution lines using sampling techniques followed the footsteps of their forerunners in the communication field. The result were circuits of considerable complexity and expense or, significantly flawed measurements.